Exact confidence intervals and hypothesis tests for parameters of discrete distributions
| Autor: | Thulin, MÅns, Zwanzig, Silvelyn |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Bernoulli 2017, Vol. 23, No. 1, 479-502 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3150/15-BEJ750 |
| Popis: | We study exact confidence intervals and two-sided hypothesis tests for univariate parameters of stochastically increasing discrete distributions, such as the binomial and Poisson distributions. It is shown that several popular methods for constructing short intervals lack strict nestedness, meaning that accepting a lower confidence level not always will lead to a shorter confidence interval. These intervals correspond to a class of tests that are shown to assign differing $p$-values to indistinguishable models. Finally, we show that among strictly nested intervals, fiducial intervals, including the Clopper-Pearson interval for a binomial proportion and the Garwood interval for a Poisson mean, are optimal. Comment: Published at http://dx.doi.org/10.3150/15-BEJ750 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm) |
| Databáze: | arXiv |
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